Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions

32 Pages Posted: 22 Aug 2017 Last revised: 21 Jul 2018

Uri Simonsohn

Ramon Llull University - ESADE Business School

Date Written: July 11, 2018

Abstract

Many psychological theories predict U-shaped relationships: the effect of x is positive for low values of x, but negative for high values, or vice-versa. Despite implying merely a change of sign, hypotheses about U-shapes are tested almost exclusively via quadratic regressions, imposing an arbitrary functional form assumption that can lead to a 100% false-positive rate, e.g., concluding with certainty that y=log(x) is U-shaped. Estimating two regression lines, one for low and one high values of x, allows testing for a sign change without a functional form assumption. To set the breakpoint between the lines, I introduce the Robin Hood algorithm. It delivers higher power to detect U-shapes than all other breakpoint setting alternatives considered. The paper includes simulations and re-analyses of published results.

Keywords: regression, interactoin, quadratic, u-shape, specification error

Suggested Citation

Simonsohn, Uri, Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions (July 11, 2018). Available at SSRN: https://ssrn.com/abstract=3021690 or http://dx.doi.org/10.2139/ssrn.3021690

Uri Simonsohn (Contact Author)

Ramon Llull University - ESADE Business School ( email )

Avinguda de la Torre Blanca, 59
Sant Cugat del Vall├Ęs, 08172
Spain

HOME PAGE: http://urisohn.com

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